First, here are a few example internships of former Princeton engineering students. The work varies widely.
Opportunities fall into a few broad categories, and are only limited by your imagination and your desire to find the opportunity.
Engineering roles in the commercial sector. Experiences most resemble full time post-graduation work experience. Successful experiences for both the student and the employer can result in offers of full time employment upon graduation. Use TigerTracks to find them. You're encouraged to find the companies that interest you through whatever means possible. Contact them and make your interests known to them.
Off-campus university research. Many universities offer research opportunities in their labs for summer students. Many of these are available through the National Science Foundation program known as Research Experiences for Undergraduates (or REUs). These are a great fit if you're considering grad school in a technical field.
On-campus university research. During the course of the year, you may become interested in working on research with a particular faculty member. You need to take the initiative to make it happen. Talk to the faculty member and ask about the possibilities.
Public service. These take many forms, from working as a staff member in a non-profit to educating children in developing countries. Many opportunities are funded by non-profit entities and require a formal application. Check out the opportunities at the PACE Center. Career Services has a list of Internships Offered by Princeton-Affiliated Organizations.
International internships. These span the commercial, university, and public service areas. Most require a formal application and leg work on your part to make them happen. See Career Services' Guide to International Internships. Additional information about International Opportunities is available on the Keller Center site. Be sure to check out Princeton's International Internship Program. To quote their site: Whether your academic focus is science, literature, history, social science, art, or engineering, your sojourn abroad – be it formal study, thesis research, or a job/internship – will enrich and expand your undergraduate education.
Additional resources. Career services also provides a list of online job search services for Engineering and Technology.